Please help me with these questions... they relate to surface area (lateral and total) and I dont understand how i a m supposed to solve it?

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2 Answers
Apr 22, 2018

#l=#3.91m
Radius=1.63m
Height=3.55m

Explanation:

#theta/360pir^2# gives the area of the sector

#=># #150/360pil^2=20#

#=># #l=sqrt(48/pi)# #l=3.9088200952#

#l=3.91m#

The length of the arc is the circumference of the cone.
#theta/360piD# gives the length of the arc
#=># #150/306pixx2xxsqrt(48/pi)#

#=># #5/6pisqrt(48/pi)# as this is the circumference of the cone we can equate it to the formula to find #r#

#=># #5/6pisqrt(48/pi)=2pir#

So #r=5/12sqrt(48/pi)# #r#=1.6286750397

To find the height of the cone use Pythagoras:
#[sqrt(48/pi)]^2-[5/12sqrt(48/pi)]^2=h^2#

#h=sqrt12.6262921519#
#h=3.5533494272#

Apr 22, 2018

The second question-see below

Explanation:

I can't see the difference between lateral and surface area on this shape so I have just done the surface area of the three parts.
The top pyramid has a height three and a length 2.5 if you go from the base of the height to the side. Thus making a right angled triangle where the hypotenuse is the height of the triangles tha make up the pyramid.
Using Pythagoras #3^2+2.5^2=h^2#

#h=sqrt(15.25)#=3.905124838

Surface area of top pyramid =4#xx1/2xx5xxh#=39.051248375

The cube =#4xx5xx5=100#

The bottom pyramid =#1/2xx5xx7.5xx4=75#